A Basis Theory Primer

Expanded Edition

Authors:

ISBN: 978-0-8176-4686-8 (Print) 978-0-8176-4687-5 (Online)

Table of contents (16 chapters)

  1. Front Matter

    Pages i-xxv

  2. A Primer on Functional Analysis

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-55

      Banach Spaces and Operator Theory

    3. No Access

      Book Chapter

      Pages 57-83

      Functional Analysis

  3. Bases and Frames

    1. Front Matter

      Pages 85-85

    2. No Access

      Book Chapter

      Pages 87-123

      Unconditional Convergence of Series in Banach and Hilbert Spaces

    3. No Access

      Book Chapter

      Pages 125-151

      Bases in Banach Spaces

    4. No Access

      Book Chapter

      Pages 153-176

      Biorthogonality, Minimality, and More About Bases

    5. No Access

      Book Chapter

      Pages 177-188

      Unconditional Bases in Banach Spaces

    6. No Access

      Book Chapter

      Pages 189-202

      Bessel Sequences and Bases in Hilbert Spaces

    7. No Access

      Book Chapter

      Pages 203-246

      Frames in Hilbert Spaces

  4. Bases and Frames in Applied Harmonic Analysis

    1. Front Matter

      Pages 247-247

    2. No Access

      Book Chapter

      Pages 249-266

      The Fourier Transform on the Real Line

    3. No Access

      Book Chapter

      Pages 267-299

      Sampling, Weighted Exponentials, and Translations

    4. No Access

      Book Chapter

      Pages 301-349

      Gabor Bases and Frames

    5. No Access

      Book Chapter

      Pages 351-425

      Wavelet Bases and Frames

  5. Fourier Series

    1. Front Matter

      Pages 427-427

    2. No Access

      Book Chapter

      Pages 429-454

      Fourier Series

    3. No Access

      Book Chapter

      Pages 455-465

      Basis Properties of Fourier Series

  6. Appendices

    1. Front Matter

      Pages 467-467

    2. No Access

      Book Chapter

      Pages 469-479

      Lebesgue Measure and Integration

    3. No Access

      Book Chapter

      Pages 481-490

      Compact and Hilbert–Schmidt Operators

  7. Back Matter

    Pages 527-536